The tire pressure monitoring system TPMS one the driver when the tire pressure of the vehicle is 27% below the target tire pressure supposed to target tire pressure of a certain car is 31 psi. (A) At what psi will the TPMS trigger a warning for this car? (B) Suppose the tire pressure is a normally distributed random variable with a standard deviation equal to two psi is the cars average tire pressure is on target what is the probability that the tea PMS will trigger a warning? (C) The manufactures recommend correct inflation range is 29 psi to 33 psi. Assume the tires average psi is on target if a tire is on the car is inspected at random what will the probability be at the tires inflation is within the recommended range?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The tire pressure monitoring system TPMS one the driver when the tire pressure of the vehicle is 27% below the target tire pressure supposed to target tire pressure of a certain car is 31 psi. (A) At what psi will the TPMS trigger a warning for this car? (B) Suppose the tire pressure is a
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